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DEVELOPMENT OF A MATLAB GRAPHICAL USER INTERFACE

FOR THE MULTI-TENSOR ANALYSIS OF DIFFUSION

MAGNETIC RESONANCE IMAGING

Inas A. Yassine, Abou-bakr A. Youssef, Yasser M. Kadah

Biomedical Engineering Department, Cairo University, Egypt,

e-mail: Inas_yassine@k-space.org

AtlStract-The estimation of diffusion tensors in diffusion tensor

imaging (DTI) is based on the assumption that each voxel is

homogeneous and can be represented by a single or multi tensor. As

a result, estimation errors arise particularly in voxels with partial

voluming of white matter or gray matter with cerebrospinal fluid

(CSF) and voxels where fibers cross. This paper presents a tool for

analysis of DTI called MultiTensor which was developed in Matlab

language in order to help DTI researchers by making the analysis

more easier and faster. The user enters the number of slices,

bvalues, the gradient directions , the number of excitations. Then

the program begin by preparing the Dicom file, estimates both

single and two tensor, the anisotropy indices and the error in

estimation.

Keywords— Diffusion Imaging, GUI, multi-tensor , magnetic

resonance Imaging.

I. INTRODUCTION

This paper presents a tool for the multi-tensor analysis of the

diffusion tensor magnetic resonance imaging (DTI) called

MultiTensor, which was developed using Matlab 7.01. This

software was designed to help the DTI researchers by making

easy to find accurate estimation of single and two-tensor, their

anisotropy indices (Fractional anisotropy. Relative Anisotropy

and Partial volume) and find the error in estimation.

This tool was developed in Matlab language provided by the

Math works Inc. software, which help in implementing the more

complex algorithms as huge matrix operations and analysis. It is

also a powerful system for Image viewing and its open source

nature allows one to adapt the software needs. The graphical

user interface (GUI) is not as easy as C^ Builders or .net

programming, but the availability of matrix analysis and graphic

functions turned Matlab into the software of choice as the

development environment for MultiTensor.

The Diffusion tensor imaging (DTI) is a non-invasive method

of characterizing tissue micro-structure. Diffusion imaging

attempts to characterize the manner by which the water

molecules within a particular location move within a given

amount of time. Using a simple pulse gradient spin echo (PGSE)

imaging sequence, it is possible to obtain a change of the MR

signal that is related to the diffusivity of water in a certain

direction. [1] The advantage of this modality lies in the fact that

the changes in water diffusion, produced by alterations in brain

biochemistry, can be observed on diffusion weighted (DW)

images long before the effects of ischemic injury can be seen on

conventional Tl, or T2 weighted images. [2] Measurement of the

diffusion tensor (D) within a voxel enables the mobility of water

to be characterized along orthotropic axes, allows a macroscopic

voxel -averaged description of fiber structure, orientation [3] and

fully quantitative evaluation of the microstructural features of

healthy and diseased tissue. [2]

II. DATASET PREPARING

The user must enters the parameters identifying the dataset as

the number of slices, the bvalues, the gradient directions and the

number of Excitations (NEX), shown in Fig. 1 , which will lead

him to browse for the directories containing the dataset. The

program must check the founding of the typical number of

DICOM figures in each folder then begin to calculate the

averages of corresponding slices with same bvalues and

directions defined in the NEX folders. As the number of NEX

increases the signal to noise ratio (SNR) decreases. The dataset

is ready now to begin the tensors estimation. Fig. 2 shows a slice

viewing after been averaged

III. ADDING NEW DATASET PARAMETERS

When loading the program for the first time, the most known

gradient combinations 6, 12 and 30 directions are added to the

program, and the same for the b-value sets. Adding new sets for

both the gradient directions and the b-value is available as

shown in fig. 3.

V datasetparameters

-Enter Dataset Parameters-

B^S

No ot Slices :

1

Gradierit Directions

Gradient Directions

l

Bvalues :

Bvalues

1

NEX:

1 1

1 0. J

Add Directions

Fig. 1 : The parameters needed for the dataset.

PROC. CAIRO INTERNATIONAL BIOMEDICAL ENGINEERING CONFERENCE 2006 '

Fig. 2 : Slice viewing after been averaged.

- New gradient Direction

Gradient name:

Numijer of Directions:

Enter Directions

Cancel

(a)

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Fig. 3: The entry of new gradient directions parameters

IV. TENSOR ANALYSIS

A- Single Tensor Estimation

The diffusion signal from a single diffusion compartment is

given by:

E(q,) = exp{-qlDq,T). (l)

where E(({k) is the normalized diffusion signal magnitude for the

diffusion gradient wave-vector qk=T8gk, T is the gyromagnetic

ratio, 6 is the diffusion gradient duration, gt is the k ' diffusion

gradient, x is the effective diffusion time, and D is the apparent

diffusion tensor. [4], [5] The output of this module is shown in

Fig. 4(b).

B- Two Tensors Estimation

Assuming a two-component model without loss of generality,

the projection along any given direction can be given as,

E(q^) = a,exp(rqlD,q^T)+a^exp(rqlD,q^T) . (2)

Here, the relative amplitudes are given by aj and a2 and the

variances are generally different for both components and vary

with projection direction. The x value is known and can be

computed given the b-value and the direction of diffusion

gradients. The ID component estimation problem amounts to the

estimation of aj, ai, D\ and D2 given £'f(jj. Notice that the

component amplitudes are the same between projections. This

property will be used to aid in the labeling of components among

different projections. This estimation problem is nonlinear and

therefore only iterative estimation methods have been proposed

[6], [7], [8]. Given the convergence issues associated with such

methods and their generally high computational burden, another

more stable strategy is needed to solve this problem in practice.

Note that for any given parameter estimation accuracy, there

exists a finite number of possible solution that are determined by

the a priori information about parameter ranges and the desired

accuracy. Hence, the problem of finding the solution to this

problem amounts to a combinatorial optimization problem. This

means that a globally optimal solution can be found by

exhaustive search or one of the more efficient random search

strategies such as simulated annealing or genetic algorithms.

Nevertheless, the computational effort involved in such

techniques is prohibitive. Here, we combine exhaustive search

and least squares estimation to obtain a more efficient

implementation while maintaining the robustness and global

optimality. In particular, instead of attempting to find all

parameters by exhaustive search, we limit this strategy to those

parameters of more importance in terms of accuracy and

compute the remaining ones using least-squares estimation. This

is implemented as follows:

Step 1. Take the variances to be the parameters estimated by

exhaustive search while the partial volume ratios are

estimated from them by least squares.

Step 2. Generate a list of possible values for the variances

within the range from to the maximum eigenvalue of the

diffusion tensors of interest with the desired accuracy as the

step.

Step 3. Plug in values for the variances in the equation from the

list and compute the least-squares solution to the

PROC. CAIRO INTERNATIONAL BIOMEDICAL ENGINEERING CONFERENCE 2006 '

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(c) Two Tensor Estimation.

partial volume ratios for such values and compute the value of

the residual error with such values plugged in.

Step 4. Loop on all possible variance values in the list and

repeat step c and find the combination of values that

generate the lowest error. Consider such combination to be

the solution.

Step 5. This method allows an order of magnitude saving in

computation time while providing a solution with sufficient

accuracy.

Once the individual component estimates from projections are

computed, the projections of each component are used to

estimate the component tensor in very much the same way as the

single tensor estimation is performed. One problem arises in this

part because of component labeling. The basic assumption of the

model that the partial volume ratios remain the same in

projections may not be practical given the superimposed noise

and other sources of error in DTI. In other words, partial volume

ratios from different projections are different in practice. To

solve this problem, an initial labeling is obtained whereby the

first component is calculated from the projection components

having the larger partial volume ratio, while the second

component is calculated from the components with the smaller

one. Once the two tensors are computed using this strategy, a

least squares estimate for the partial volume ratios is computed

while imposing the constraint of unit summation upon their

values. Then, the calculated values are used in a second iteration

of the procedure above to update the projection variances while

imposing the same partial volume ratios obtained from the first

iteration. A second estimate of the partial volume ratios is

computed at the end of the second iteration and this process is

repeated until estimates from two successive iterations come out

within a predetermined tolerance. In this case, the estimates

represent the global solution that is not be biased by error within

individual projections.

It should be noted that the extension of this method to multiple

exponential is straight-forward. The computational complexity

of the developed method can be shown to depend linearly on the

number of components. This allows the possibility of addressing

more challenging tasks. We still gain the separation between the

problems of estimating the variances and the magnitudes.

Moreover, the same direct magnitude estimation method can still

be applied in this case once the roots are calculated. This can, at

least in principle, reduce the require complexity dramatically.

[9], [10] The output of this module is shown in Fig. 4(c).

V. ANISOTROPY INDICES

Several scalar indices have been proposed to characterize

diffusion anisotropy. Initially, simple indices, calculated from

diffusion weighted images or apparent diffusion coefficients

(ADCs) obtained in perpendicular directions were used [8]. They

are clearly dependent on the choice of directions made for the

measurements. The degree of anisotropy would then vary

according to the respective orientation of the gradient hardware

and the tissue frames of reference and would generally be

underestimated. Here again, invariant indices must be found to

avoid such biases and provide an objective, intrinsic structural

information [11].

PROC. CAIRO INTERNATIONAL BIOMEDICAL ENGINEERING CONFERENCE 2006 '

Invariant indices are thus made of combinations of the terms

of the diagonahzed diffusion tensor, i.e., the eigenvalues X-i, X2

and X3. The most commonly used invariant indices are the

relative anisotropy (RA), the fractional anisotropy (FA), and the

volume ratio (VR) indices, defined respectively as:

FA--

RA

3[i\-Af + iA,-Af + (A,

-Af]

2(A-

-^-

4)

V[(A-^)'+(^-^)'+(^-^)']

VR

V3/1

(3)

(4)

(5)

The FA measures the fraction of the magnitude of D that can

be ascribed to anisotropic diffusion. The RA, a normalized

standard deviation, also represents the ratio of the anisotropic

part of D to its isotropic part. FA and RA vary between

(isotropic diffusion) and 1(=2 for RA) (infinite anisotropy). As

to the VR, it represents the ratio of the ellipsoid volume to the

volume of a sphere of radius equal to the average eigenvalue and

its range is from 1 (isotropic diffusion) to [12].

VI. ERROR IN ESTIMATION

The error in Estimation was then calculated from the

following Equation:

Error=^ ±Z(S(h,,q,)-S(b„q,)f

1/ V !=1 k=l

(6)

where S(bj,qj) is the original signal used in Estimation and

S(bj,(/j) is the predicted diffusion signal based on the

single/multi tensor model. The output of Error in estimation is

shown in Fig. 5.

File Edit Vlsw Dataset Solve Window Help |

VII. CONCLUSION

This paper presented a powerful tool for analysis of Diffusion

tensor images called MultiTensor. This software, which was

developed using Matlab 7.01, helps the Diffusion tensor

researchers as providing the estimation of the tensors that can be

used next in any other application as the fiber tracking. The choice

of using Matlab will also allow others to modiiy and improve

MultiTensor, making it even more versatile.

REFERENCE

[I] P. J. Basser, C. Pierpaout, "Microstructural and physiological

features of tissues elucidated by quantitative diffusion-tensor MRl,"/,

Magn. Reson. B 1 11. pp. 209-219, 1996.

[2] M. E. Bastin, P. A. Armitage, I. Marshall, "A Theoretical Study of

the effect of experimental noise on the measurement of anisotropy in

Diffusion Imaging," Magn. Reson. Imag. 16, no. 7, pp. 773-785, 1998.

[3] P.A. Armitage, M.E. Bastin, "Utilizing the diffusion-to-Noise ratio

to optimize magnetic resonance diffusion tensor acquisition strategies

for improving measurements of diffusion anisotropy," Magn. Reson.

MBd45, pp. 1056-1065, 2001.

[4] P. J. Basser, D. K. Jones, "Diffusion-tensor MRI: theory,

experimental design and data analysis- a technical review," NMR

Biomed., vol. 15, pp. 456-467, 2002.

[5] P. J. Basser, "New histological and physiological stains derived

from diffusion-tensor MR images," Annals New York Academ]i of

Science, vol. 820, pp.526-540, 1999.

[6] D.S. Tuch, T.G. Reese, M.R. Wiegell, N. Makris, .T.W. Belliveau,

and V.J. Wedeen, "High angular resolution diffusion imaging reveals

intravoxel while matter fiber heterogeneity," Magn. Reson. Med. 48, pp.

577-582, 2002.

[7] P.J. Basser and D.K. Jones, "Diffusion-tensor MRI: theory,

experimental design and data analysis - a technical review," NMR

Biomed. 15, pp. 456-467, 2002.

[8] E.W. Hsu, D.L. Buckley, J.D. Bui, S.J. Blackband, and J.R.

Forder, "Two-compartment diffusion tensor MRI of isolated

perfused hearts," Magn. Reson. Med. 45, pp. 1039: 1045, 2001 .

[9] Y. M. Kadah, X. Ma, S. LaConte, I. Yassine, X. Hu, "Robust multi-

component modeling of diffusion tensor magnetic resonance imaging

data", Proc. SPIE Medical Imaging 2005, Feb. 2005.

[10] I. A. Yassine, A. M. Youssef, Y. M. Kadah ,"Novel

Methods for resolving diffusion tensor magnetic resonance

imagmg", Proc. URSI 2006, March 2006.

[II] D. LeBihan, J. F. Mangin, C. Poupon, C. A. Clark, S. Pappata, N.

Molko, H. Chabriat, "Diffusion tensor imaging: concepts and

applications," J. Magn. Reson., Imag., vol. 13, pp. 534-546, 2001.

[12] P. J. Basser, C. Pierpaout, "Microstructural and physiological features

of tissues elucidated by quantitative diffusion-tensor MRI," J . Magn.

fleson., series B, vol. Ill, pp. 209-219, 1996.

Fig. 5: Scaled en'or.

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